Question

Find the value of a and b so that $8x^4+14x^3-2x^2+ax+b$ is exactly divisible by $4x^2+3x-2$.

Answer 1

$8x^4+14x^3-2x^2+ax+b$ is divisible by $4x^2+3x-2$

$2x^2+2x-1$

$4x^2+3x-2)8x^4+14x^3-2x^2+ax+b$

$8x^4+6x^3-4x^2$

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$8x^3+2x^2+ax$

$8x^3+6x^2-4x$

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$-4x^2+x(a+4)+b$

$-4x^2-3x+2$

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$x(9+4+3)+b-2$

$x(9+4+3)+(b-2)=0$ (for exactly divisible)

$9+4+3=0$, $b-2=0$

$a=-7$

$b=2$.